does there exist a fraction, which is in lowest terms, x/y such that in which y>x and

x/y=.abcabcabcd s.t. 1≤a≤8
5≤b≤9
0≤c≤9
d=a+1

Zacho - perhaps I don't quite understand what you're getting at, but if you pick any values you want for a,b,c, and d that satisfy your constraints you have a decimal of fixed length, and any decimal of fixed length can always be expressed as a fraction. For example, suppose you set a=4, b=6, c=2: then d = 5 and you have:

x/y = .4624624625
So x = 4,624,624,625and y = 10,000,000,000

This can be reduced to a proper fraction with no common factors between the numerator and denominator - in his case you can divide top and bottom by 125 to get:
36,996,997/80,000,000